Abstract: Vague relations as generalized fuzzy relations are more powerful to express fuzzy information than fuzzy relations. Based on the vague set theory, the vague relations and relevant compositional operations are systemically studied by introducing the definitions of vague sets/norms and their properties so as to give the definitions of general relations between vague sets including reverse, null and identical relations. Then, the properties of the relational operations between them and related theorems are studied with necessary proofs given. Furthermore, the t-norms and s-norms are introduced into the compositional operations of vague relations with relevant theorems and proofs given. Thus, the application of the composite operation to making up for the missing data in approximate vague relations via max-t and min-5 composite is discussed.